The Lunatic AI lasts indefinitely. Or rather, it doesn't weaken over time. It has to get unlucky and trap itself to get hit. Having said that, Marisa's lasers are somewhat capable of trapping it, though Aya's speed probably makes her harder to hit than any other character. Her attacks are relatively easy to avoid, at least. Ultimately you'll need extreme luck to beat her.
About your second question, I'm not sure what you're asking. As far as I'm aware, the speed of a reflected bullet is determined by (perhaps even identical to) the speed at which it was initially fired. It doesn't matter who reflected them. So things like Reimu's lvl2 or Eiki's boss attack get sent back super fast, while Medicine's stuff is very slow, etc.
So I did another No-Bomb run in PoDD last night. This time with Reimu, on the first try after the Rikako run. I even had an extra life remaining. I guess Kotohime's my next target. She has the advantage of safe boss attacks and a demonic lvl1, but it'll take forever to win battles. Mima is also a possibility.